1. Field of the Invention
The present invention relates generally to a method of compensating the output of an air/fuel ratio sensor, and more particularly, to such a compensating method suitably applicable to a control system associated with a sensor which is adapted to measure an excess or shortage amount of oxygen in an exhaust gas emitted from an internal combustion engine of a motor vehicle or from an industrial furnace, to thereby determine an air/fuel ratio of an air-fuel mixture which produces the exhaust gas. The invention is concerned with such a sensor output compensating method that assures improved accuracy of determination of the air/fuel ratio of the air-fuel mixture.
2. Discussion of the Prior Art
In the art of measuring the air/fuel ratio of an air-fuel mixture supplied to an automotive internal combustion engine or an industrial furnace, it is generally practiced to measure the concentrations of the components (e.g., O.sub.2, CO.sub.2, CO, H.sub.2 and HC) of the exhaust gas produced as a result of combustion of the air-fuel mixture, for calculating or determining the air/fuel ratio of the mixture based on the measured concentrations. For measuring the concentration of O.sub.2 in the exhaust gas, there has been widely used an air/fuel ratio sensor in the form of an electrochemical sensing element of a so-called single-cell type which is operated according to the principle of an oxygen concentration cell. In recent years, there is available a so-called double-cell type air/fuel ratio sensor which includes an electrochemical cell operated according to the principle of the oxygen concentration cell, and another electrochemical cell adapted for performing an oxygen pumping action. This double-cell type sensor is advantageous for its improved accuracy of determination of the air/fuel ratio (A/F ratio) of the air-fuel mixture, based on a known relationship between the concentrations of the components of the exhaust gas produced by the combustion of the air-fuel mixture, and the output value of the sensor (more precisely, the oxygen pumping current applied to the pumping cell).
The double-cell type electrochemical sensor has a sensing element which includes two electrochemical cells each having at least one pair of electrodes disposed on an oxygen-ion conductive solid electrolyte body. The sensing element has an internal space formed between the two cells so that an exhaust gas under examination is introduced under a predetermined diffusion resistance. The first electrochemical cell (referred to as "sensing cell"), which is operated according to the principle of an oxygen concentration cell, produces an electromotive force induced according to the Nernst equation, depending upon the oxygen partial pressure in the atmosphere in the internal space. 0n the other hand, the second electrochemical cell (referred to as "pumping cell") is operated to perform an oxygen pumping action to change the oxygen partial pressure in the internal space so that the electromotive force coincides with a level which corresponds to an excess oxygen ratio or excess air ratio (.lambda.) of 1 (.lambda.=1). The pumping current applied to the pumping cell to establish the excess oxygen ratio of 1 is used as the output of the air/fuel ratio sensor, which varies with the components of the exhaust gas.
In the single-cell type air/fuel ratio sensor indicated above, the output E (electromotive force) changes with the oxygen partial pressure of the exhaust gas, according to the following Nernst equation (i): ##EQU1## where, E: electromotive force of A/F ratio sensor (sensing element thereof),
R: gas constant (Gas-law constant), PA1 Tc: temperature of the sensing element PA1 n: number of ions, PA1 F: Faraday constant (faraday), PA1 Po.sub.2 (I): oxygen partial pressure of reference gas, PA1 Po.sub.2 (II): oxygen partial pressure of exhaust gas. PA1 Ko.sub.2 : Current sensitivity coefficient of oxygen concentration, PA1 Po.sub.2 (II): O.sub.2 partial pressure of exhaust gas, PA1 Kco: Current sensitivity coefficient of CO concentration, PA1 Pco: Co partial pressure of exhaust gas, PA1 K.sub.H.sbsb.2 : Current sensitivity coefficient of H, concentration, and PA1 P.sub.H.sbsb.2 : H.sub.2 partial pressure of exhaust gas. PA1 CmHn: Carbon/hydrogen fuel PA1 m: molar number of carbon component in 1 mole of the fuel, PA1 n: molar number of hydrogen component in 1 mole of the fuel, PA1 .lambda.: excess air ratio, PA1 A.sub.1 .about.A.sub.6 : molar numbers of the relevant components of the exhaust gas, the values A.sub.1.CO and A.sub.3.H.sub.2 being approximately 0% where .lambda.&gt;1, while the values A.sub.1.CO and A.sub.3.H.sub.2 being not 0% where .lambda.&lt;1. PA1 P.sub.H.sbsb.2.sub.O : H.sub.2 O partial pressure of exhaust gas, PA1 P.sub.CO.sbsb.2 : CO.sub.2 partial pressure of exhaust gas, and PA1 P.sub.H.sbsb.2 : H.sub.2 partial pressure of exhaust gas. In the single-cell type air/fuel ratio sensor designed to determine the A/F ratio of the air-fuel mixture based on its output, the value of the output is influenced by a variation in the temperature of the electrochemical sensing element and the pressure of the exhaust gas, as is understood from the Nernst equation, whereby the variation of the temperature and pressure results in an error in the A/F ratio as determined based on the output value, even if the oxygen partial pressure of the exhaust gas is constant. This phenomenon is theoretically apparent. In the known sensor, the error in the sensor output due to the variations in the temperature of the sensing element, pressure of the exhaust gas and other parameters is inevitable or unavoidable. At present, there is no such single-cell type A/F ratio sensors that are capable of dealing with the exhaust gas which is produced as a result of a fuel-rich air-fuel mixture whose A/F ratio is lower than the stoichiometric point. PA1 TCo: reference temperature of the sensing element, and PA1 A: temperature variation index measured at the sensing element. PA1 Pgo: reference pressure of the exhaust gas, and PA1 B: variation index of the exhaust gas pressure measured for the sensing element. PA1 F: Faraday constant, and PA1 Pgo: reference pressure of the exhaust gas. PA1 A: temperature variation index measured at the sensing element, PA1 Pgo: reference pressure of the exhaust gas, and PA1 B: pressure variation index measured at the sensing element. PA1 Tco: reference temperature of the sensing element, PA1 R: gas constant, PA1 F: Faraday constant, and PA1 Pgo: reference pressure of the exhaust gas. PA1 L: gas diffusion length through the sensing element, and PA1 C: molar concentration of the component. PA1 Ipo: output of the sensor at Tco, PA1 A: temperature variation index measured at the sensing element PA1 B variation index of the exhaust gas pressure measured for the sensing element. PA1 Pgo: reference pressure of the exhaust gas, PA1 Ipo: sensor output at Tco and Pgo, PA1 A: temperature variation index measured at the sensing element, and PA1 b: variation index of the exhaust gas pressure measured for the sensing element.
In the double-cell type air/fuel ratio sensor (which may be a type in which the sign of the voltage applied to the pumping cell is reversed depending upon the output of a TiO.sub.2 sensor adapted to determine whether the air/fuel mixture which produces the exhaust gas is a fuel-lean mixture or a fuel-rich mixture), the output Ip (pumping current) changes with the partial pressures of O.sub.2, CO and H.sub.2 of the exhaust gas, according to the following equation (ii): EQU Ip=Ko.sub.2.Po.sub.2 (II)-Kco.Pco-K.sub.H.sbsb.2.P.sub.H.sbsb.2 (ii)
where,
The components of the exhaust gas are obtained by comparison of reaction molar numbers before and after the combustion of the air-fuel mixture, as indicated by the following equations (iii-1) and (iii-2):
a) Before combustion EQU CmHn+.lambda.{O.sub.2 +(m+n/4).(79.05/20.95).N.sub.2 } (iii-1)
After combustion EQU A.sub.1.CO+A.sub.2.CO.sub.2 +A.sub.3.H.sub.2 +A.sub.4.H.sub.2 O+A.sub.5.O.sub.2 +A.sub.6.N.sub.2 (iii- 2)
where,
Therefore, the relationship between the sensor output, and the oxygen concentration of the exhaust gas, or the excess air ratio or A/F ratio of the air-fuel mixture can be obtained directly by experiments, or by approximating calculation, by using in the above equations (iii-1) and (iii-2) a water gas reaction coefficient K(t) represented by the following equation (iv): ##EQU2## where, Pco: CO partial pressure of exhaust gas,
On the other hand, the double-cell type A/F ratio sensor is capable of determining the A/F ratio of the air-fuel mixture even where the A/F ratio changes from a fuel-lean range to a fuel-rich range, across the stoichiometric point. For this reason, the double-cell type A/F ratio sensor is increasingly used. However, it is recognized that this double-cell type A/F ratio sensor also suffers from an error in the output value or the A/F ratio determined, due to the variations in the temperature of the sensing element (sensing and pumping cells) and the temperature and pressure of the exhaust gas.
Up to the present, no effective methods are available for compensating the sensor output for the variations in the sensor temperature and the exhaust gas temperature and pressure. Namely, these fluctuating parameters have been treated as being constant, in determining the A/F ratio of the air-fuel mixture, whereby the resulting error has been inevitable.
In the light of the above drawbacks experienced in the prior art, there is a long-felt need for improving the accuracy of measurement or determination of the A/F ratio, in particular, in view of the recent growing requirements for more stringent regulation of the exhaust emission from an automotive internal combustion engine, and for further enhancement of the fuel economy of the vehicle.